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INMO 2019 Discussion

This is the place where we may discuss various problems and get updates of INMO 19. I expect the students of different states to post some problems discussed in their INMOTC. I will regularly upload some problems and even practice tests for INMO and expect you to do so too. Hope we all do perform well in INMO and many of us may even get selected for INMO

IN MY NEXT POST, I WILL SEND A MOCK TEST A BIT EASIER THAN INMO, AS IT IS JUST THE BEGINNING.

1.A circle passes through the vertex C of a rectangle ABCD and touches its sides AB and AD at M and N respectively If the distance from C to the line segment MN is 5 units, find the area of ABCD.
2.Consider the set {3,5,7,9}. You can choose any 2 numbers a,b and replace them by (4a+3b)/5 and (3a-4b)/5. Prove that you can never get the set {2,3,4,9}.
3.A 3*3 square is said to be a mystic square if
i)Its entries are from 1 to 13(both inclusive, repetition allowed)
ii)The sum of any row, column or diagonal is always divisible by 13.
Find the number of MYSTIC SQUARES.
4.In a triangle ABC, AB=AC and angle A is 20 degrees.D is chosen on AC such that AD=BC.Without using trigonometry, find angle ABD.
5.Let P(x) be a cubic polynomial function with positive coefficients..Prove, if -1≤P(x)≤1 for all x such that -1≤x≤1, prove that sum of coefficients of P(x) is at most 7.
6.Find all functions f:R to R which obey
f((x-y)²)=f(x)²-2xf(y)+f(y)²

Yeah problem no 6 looked easy but solving it took me complete hour and mind bending brainstorming and I skipped two or three lemmas and messed everything but solved it. Seems they would care to give 2 or 3 marks.

Hey everyone. I appeared for INMO 2019 and solved P2 and P3. In P6, I managed to provide a "pseudo-proof" that f(x,y) =1. What are my chances of selection?
Also, I couldn't solve P1 but I heard many saying that it was the easiest problem. Is this really the case?

Hey dude........same case over here...........I mean even I have done the EXACT same things except P6, in which I was only able to prove the first part..........Oh well.......Chances are slim...........And Yes, P1 was the easiest......IDK why it did not strike me during the exam........!!!!